been forever since I have logged onto this site, but I do have some experience in brambles.
If the brambles are really thick, they will need to be broken up with a spade/long stick to a more manageable size. Generally under the new green growth it is just dead bramble. Once you have hit them down to about waist/knee height, you can pile them up and burn them where they are, or you can just move them to the side, they rot down fairly quickly.
Depending on how much time/effort you want to spend, you can either dig out the roots if they are really big, or just cover them with a tarp, which should kill them eventually.
But if you are at the trails often, it is quite easy to just dig up any roots which are sprouting, and they should be gone reasonably quickly.